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arXiv 0709.3835quant-ph
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关联纠缠蒸馏与不可分离态集的结构

Correlated entanglement distillation and the structure of the set of undistillable states

Fernando G. S. L. Brandao, Jens Eisert

摘要:

我们考虑纠缠蒸馏的假设下,允许输入状态之间的相互关联。因此,我们用仅仅具有相同约简的较弱假设来取代通常考虑的独立和同分布假设。我们发现,一个状态是否可归约仅仅是这些归约的性质,而不是输入状态中存在的相关性的性质。这是通过建立一个吸引人的关系之间的集合的复制相关的不可分割的状态和不可分割的状态的标准集:前者原来是后者的凸包。作为一个例子,我们的方法来研究纠缠蒸馏的有用性,我们证明了一个新的激活结果,它概括了以前的发现:它表明,对于每个纠缠态和每个正整数k,存在一个副本相关的k-不可分解的状态,使它们的张量积是单副本可分解的。最后,讨论了我们的结果与部分转置非正束缚纠缠态存在性猜想的关系。

英文摘要:

We consider entanglement distillation under the assumption that the input states are allowed to be correlated among each other. We hence replace the usually considered independent and identically-distributed hypothesis by the weaker assumption of merely having identical reductions. We find that whether a state is then distillable or not is only a property of these reductions, and not of the correlations that are present in the input state. This is shown by establishing an appealing relation between the set of copy-correlated undistillable states and the standard set of undistillable states: The former turns out to be the convex hull of the latter. As an example of the usefulness of our approach to the study of entanglement distillation, we prove a new activation result, which generalizes earlier findings: it is shown that for every entangled state and every positive integer k, there exists a copy-correlated k-undistillable state such that their tensor product is single-copy distillable. Finally, the relation of our results to the conjecture about the existence of bound entangled states with a non-positive partial transpose is discussed.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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